Tensor Density Estimator by Convolution-Deconvolution
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915580487925760 |
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| author | Peng, Yifan Yang, Siyao Khoo, Yuehaw Wang, Daren |
| author_facet | Peng, Yifan Yang, Siyao Khoo, Yuehaw Wang, Daren |
| contents | We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the empirical distribution after convolution as a tensor train, with efficient tensor decomposition algorithms; and finally, applying a deconvolution step to recover the estimated density from such tensor-train representation. Numerical results demonstrate the high accuracy and efficiency of the proposed methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18964 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Tensor Density Estimator by Convolution-Deconvolution Peng, Yifan Yang, Siyao Khoo, Yuehaw Wang, Daren Numerical Analysis 15A69, 62Gxx We propose a linear algebraic framework for performing density estimation. It consists of three simple steps: convolving the empirical distribution with certain smoothing kernels to remove the exponentially large variance; compressing the empirical distribution after convolution as a tensor train, with efficient tensor decomposition algorithms; and finally, applying a deconvolution step to recover the estimated density from such tensor-train representation. Numerical results demonstrate the high accuracy and efficiency of the proposed methods. |
| title | Tensor Density Estimator by Convolution-Deconvolution |
| topic | Numerical Analysis 15A69, 62Gxx |
| url | https://arxiv.org/abs/2412.18964 |